A Practical Quadrature – Collocation Method to Solve Frictional Contact Problems

Elçin Yusufoğlu¹, Hüseyin Oğuz²

1. Usak University, Usak, Turkey, elcin.yusufoglu@usak.edu.tr

2. Dumlupinar University, Kutahya, Turkey, huseyin.oguz@dpu.edu.tr

Abstract: The contact problem of impressing absolutely rigid punch under normal and shear forces into an elastic layer is examined in presence Coulomb friction in the contact area. It is assumed that the lower boundary of the layer is fixed or there are no normal displacements and shear stresses on it, the punch-strip system is in a condition of limit equilibrium, and the punch does not turn during deformation of the layer. First, considered contact problem is reformulated by Cauchy type singular integral equation of the second kind in which the unknown is the normal contact stresses beneath the punch, next this equation is reduced to system linear algebraic equations by using Gauss-Jacobi quadrature and collocation methods. The effects of geometrical and mechanical parameters of the materials on various subjects of interest are discussed and shown graphically and tabular form.

Keywords: Singular Integral Equation, Plane Contact Problem, Cauchy kernel, Jacobi polynomial, A system of linear algebraic equation.

Pages: 385 – 395 | Full PDF Paper